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Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function which is defined as the largest power of k dividing x, named in honor of the Swiss mathematician Julius Richard Büchi. The signature of Büchi arithmetic contains only the addition operation, and equality, omitting the multiplication operation entirely.

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  • Büchi arithmetic (en)
  • Aritmética de Büchi (pt)
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  • Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function which is defined as the largest power of k dividing x, named in honor of the Swiss mathematician Julius Richard Büchi. The signature of Büchi arithmetic contains only the addition operation, and equality, omitting the multiplication operation entirely. (en)
  • Aritmética de Büchi de base k é a teoria de primeira ordem dos números naturais com adição e a função que é definida como a maior potência de k dividindo x, denominado em homenagem ao matemático Suíço Julius Richard Büchi. A assinatura da aritmética de Büchi contém apenas a operação de adição, e a igualdade, omitindo-se a operação de multiplicação inteiramente. (pt)
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  • Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function which is defined as the largest power of k dividing x, named in honor of the Swiss mathematician Julius Richard Büchi. The signature of Büchi arithmetic contains only the addition operation, and equality, omitting the multiplication operation entirely. Unlike Peano arithmetic, Büchi arithmetic is a decidable theory. This means it is possible to effectively determine, for any sentence in the language of Büchi arithmetic, whether that sentence is provable from the axioms of Büchi arithmetic. (en)
  • Aritmética de Büchi de base k é a teoria de primeira ordem dos números naturais com adição e a função que é definida como a maior potência de k dividindo x, denominado em homenagem ao matemático Suíço Julius Richard Büchi. A assinatura da aritmética de Büchi contém apenas a operação de adição, e a igualdade, omitindo-se a operação de multiplicação inteiramente. Ao contrário da aritmética de Peano, a aritmética de Büchi é uma teoria decidível. Isto significa que é possível, efetivamente, determinar para qualquer sentença na linguagem da aritmética de Büchi, se essa sentença é demonstrável a partir de axiomas da aritmética de Büchi . (pt)
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